The Method of Coordinates,9780486425658

The Method of Coordinates

by ; ;
ISBN13: 9780486425658
ISBN10: 0486425657
Format: Paperback
Pub. Date: 2011-10-20
Publisher(s): Dover Publications
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Summary

This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space. Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of "road signs" in the margins, alerting students to passages requiring particular attention, and an abundance of ingenious problemswith solutions, answers, and hintspromote habits of independent work. 1967 edition.

Table of Contents

Foreword v
Introduction 1(4)
PART 1
The Coordinates of Points on a Line
5(7)
The Number Axis
5(3)
The Absolute Value of a Number
8(1)
The Distance Between Two Points
9(3)
The Coordinates of Points in the Plane
12(20)
The Coordinate Plane
12(3)
Relations Connecting Coordinates
15(2)
The Distance Between Two Points
17(3)
Defining Figures
20(3)
We Begin to Solve Problems
23(4)
Other Systems of Coordinates
27(5)
The Coordinates of a Point in Space
32(9)
Coordinate Axes and Planes
32(4)
Defining Figures in Space
36(5)
PART 2
Introduction
41(9)
Some General Considerations
41(1)
Geometry as an Aid in Calculation
42(3)
The Need for Introducing Four-Dimensional Space
45(2)
The Peculiarities of Four-Dimensional Space
47(1)
Some Physics
48(2)
Four-Dimensional Space
50(8)
Coordinate Axes and Planes
51(5)
Some Problems
56(2)
The Four-Dimensional Cube
58(9)
The Definition of the Sphere and the Cube
58(2)
The Structure of the Four-Dimensional Cube
60(7)
Problems on the Cube
67

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